SPEAR: A Monopedal Robot with Switchable Parallel Elastic Actuation

Transcription

1 SPEAR: A Monopedal Robot with Switchable Parallel Elastic Actuation Xin Liu, Anthony Rossi and Ioannis Poulakakis Abstract Inspiredbybiologicalsystems,compliantelements are introduced in the driving train of legged robots with the purpose of recycling energy. This paper presents the design and control concept of the monopedal robot SPEAR, driven by a novel implementation of a Switchable Parallel Elastic Actuator (S-PEA). At the stance phase, the parallel spring in S-PEA works with the actuator to support body weight and recover energy. The spring is removed from the system at the flight phase to gain precise joint control. The stiffness of the whole leg is also adjustable online either by active control of the motor or by changing the knee angle at touchdown. Experimental results show that the spring recycles part of energy during hopping, reducing the peak torque and peak power of the motor. Encoders Cable Drive S Motors S 1 τ Hip Torso S 1 -θ Hip Spacer S τ Knee θ Knee I. INTRODUCTION Running robots typically operate in regimes where the natural dynamics of the mechanical system imposes strict limitations on the capability of the motor units to guide the robot s motion. Furthermore, the pressure for extended power autonomous operation calls for increased energy efficiency, thereby making excessive reliance on the motors even undesirable. To address these challenges, a series of actuator designs has been introduced; the majority of these actuators combine elastic energy storage elements with motors to generate and sustain highly-dynamic running motions [1]. Awidelyadoptedapproachtointroducingcompliancein the robot s structure is to insert a spring into the driving train in series with an actuator [1], []. An early implementation of series compliance can be found in Raibert s robots, in which air springs were placed in series with hydraulic actuators [3]. The bipedal robot MABEL [4] is designed with large leaf springs connected in series with the actuators through a transmission system so that compliance is present in the leg length direction [5]. Inspired by the Series Elastic Actuator (SEA) architecture [], the StarlETH comprises 1 SEAs actuating all of its joints [6]. An advantage of inserting springs in series with the actuators is that they offer protection of the motors and gearboxes by filtering out the instantaneous change in velocity when the a leg impacts with ground. However, SEAs typically increase the number of degrees of freedom (DOF) of the system. Moreover, with the aim to store energy, the springs are usually large and the motors need to produce forces or torques that have similar magnitudes as the ones developed by the springs [7]. An alternative way to introduce compliance is to insert the spring in parallel with the motor. An attractive feature of this This work is supported in part by NSF grant CMMI and ARO contract W911NF The authors are with the Department of Mechanical Engineering, University of Delaware, DE, USA; {xinliu, avrossi, poulakas}@udel.edu Foot γ Foot Cable Fig. 1. The manufactured leg. A cable-pulley system is used to move the knee actuator more close to the hip axis. The schematic drawingof the robotic leg. One end of the large spring S 1 is attached to the thigh by asteelcable, whiletheotherendfirstpassthroughthekneespacer, then pass through the foot (at this part, the cable is replaced by a roller chain), then attached to the shank by the small spring S. configuration is that the spring provides most of the torque required at the joint to maintain a desired motion, while the motor can modify the torque profile as needed to stabilize the system [8]. An example of using Parallel Elastic Actuators (PEA) can be found in [7], where springs are used to improve energy efficiency and safety of known maneuvers in passiveassist devices for active joints. In the context of legged robots, the biped ERNIE utilizes springs in parallel with its knee actuators to generate walking motions [9]. PEAs may reduce both power and torque requirements, as suggested in simulations of bipedal [1], [11] and quadrupedal robot [1] running. The recent results in [13] provide a comparison between SEAs and PEAs in terms of energy efficiency. In general, introducing springs in parallel with the actuators may limit joint dexterity in the sense that the actuator needs to work against the spring [14]. To overcome the drawback of PEAs, the concept of Switchable Parallel Elastic Actuator (S-PEA) has been suggested in the relevant literature [8]. According to this concept, a switch which can be a brake, a clutch or a trigger mechanism is used to engage the spring when energy storage is desired and disengage it to avoid the spring force interfering with the desired joint motions [14]. The case of a knee joint actuated by a S-PEA is considered in [8], where a mechanism with position-dependent clutch function is proposed to engage the spring when it is needed; that is, during the stance phase. AconceptualdesignofaS-PEAisalsoproposedin[1]

2 to reduce the energy requirement of quadrupedal running. However, to the best of the authors knowledge, only [14], [15] realized S-PEA designs in hardware, to explore its potential in terms of energy efficiency. Experiments suggest that the energy consumption is dropped by 8% and the peak torque requirement is dropped by about 66%. In this paper, we investigate how the S-PEA architecture can be used in the context of dynamic legged locomotion. We present the conceptual design and hardware realization of the Switchable Parallel Elastic Actuator Robot (SPEAR), atwo-doflegthatemploysas-peaatitskneejointand is suitable for dynamic locomotion; see Fig. 1. SPEAR features a mechanical switch at its foot, which engages the spring only when the leg is on the ground, thereby recycling part of the energy during the compression and decompression phases of the stance. During flight, the switch disengages the spring and the motor can place the leg at a desired configuration in anticipation to touchdown without interfering with the spring. With this mechanical switch, the S-PEA is automatically synchronized with the hopping motion, and it requires no additional actuators to control the switch, thereby resulting in a reliable and compact design. Finally, we design and experimentally implement simple control laws that take advantage of the S-PEA to realize stable hopping motions in order to evaluate the performance of SPEAR in terms of peak power and peak torque requirements. A video showing the experimental implementation of hopping motions on SPEAR accompanies this paper. II. DESIGN OF SPEAR This section discusses the basic principle that underlies our Switchable Parallel Elastic Actuator (S-PEA) design, and the hardware realization of a robot leg, the knee joint of which is actuated by the S-PEA. A. Working Principle of S-PEA Introducing compliance in running robots is a necessary, albeit challenging task [1]. This is primarily due to the different objectives that the mechanical system needs to satisfy at different phases of the motion. For example, when a leg is in contact with the ground, compliant members are important in supporting body weight and storing energy during the initial stages of the stance, which is subsequently released to prepare the system for takeoff. On the other hand, when the leg is in the air, compliant elements are undesirable, for they may interfere with leg placement in anticipation to touchdown by introducing oscillations that impede joint motion and precise positioning. To address this challenge, we propose the S-PEA, a new actuator design that engages compliance in parallel with amotoronlywhenelasticenergystorageisneeded.the principle that underlies the proposed design is shown in Fig., in which the joint that connects Link A and Link B is composed of an actuator and a compliant element connected in parallel. The compliant element comprises two springs S 1 and S connected through a mechanical switch realized by a key and a chain as shown in Fig. -(c). Link A Foot(Key) Key S S 1 GRF actuator To S S 3 To S 1 chain Link B (c) Fig.. The schematic of the proposed S-PEA design. The stiffness of the joint is determined by the status of the Key. The section view of the foot which functions as the Key in. Here the foot is inserted into the chain by the ground reaction force (GRF) and spring S 1 is engaged. S 3 is asmallspringusedtokeepthefootunpluggedfromthechainwhen there is no GRF. The contact switch is used to determine if the foot is inserted in the chain. (c) The manufactured foot. S 3 Contact Switch The two springs have different stiffnesses; the spring S 1 has stiffness K 1 and the spring S has stiffness K and is much softer than S 1 ;i.e.,k 1 K.Theeffectivestiffness of the combined springs is determined by the status of the key. When the key is inserted in the chain, the mechanical switch is closed and the hard spring S 1 is connected to Link A; inthisconfiguration,theeffectivestiffnessofthe joint is K 1,favoringenergystorage.Whenthekeyisnot inserted in the chain, the springs S 1 and S are connected in series, and the effective stiffness of the joint is mostly determined by the softer spring and is, in fact, smaller than K.WithK negligible, the hard spring S 1 is considered to be switched off. As a result, this configuration favors precise joint motion control via the actuator. In fact, the small spring S is used merely to keep the tension in the compliant element. B. SPEAR: A leg design that uses the S-PEA SPEAR is a planar monopedal robot composed of two links representing the thigh and the shank of a kneed leg that is terminated at a point foot as shown in Fig. 1. The thigh is connected to a torso via the hip joint with a range of motion in [ 85, 85 ],whilethethighandshank are connected by the knee joint with a range of motion [ 1, 14 ]. The robot s torso is rigidly connected to a boom as discussed in Section II-E below. The knee joint of the SPEAR is driven by the proposed S-PEA, as shown in Fig. 1. In our realization, the S-PEA engages the hard spring S 1 during the stance phase, thereby harnessing its elastic energy storage capability when it is

3 needed. During the subsequent flight phase, S 1 is disengaged allowing the actuator to shorten or lengthen the leg without interfering with the spring. In more detail, one end of the hard spring S 1 is attached to the thigh by a steel cable. The other end of S 1 first passes through the circular knee spacer, which is rigidly attached to the shank, then passes through the foot and is attached to the other side of the shank by a soft return spring S.Although asolenoidcouldhavebeenusedtocontrolthepull/push reaction of the key in the S-PEA, in our implementation the foot acts as the key and is used to engage and disengage the spring S 1 depending on the state of the leg; see Fig. and Fig. (c). The foot has a tooth shape at one end, and is connected to the shank by a prismatic joint which allows the foot to have a maximum range of motion of 1cm. Duringthe stance phase, when the foot is in contact with the ground, the ground reaction force pushes the key inside the chain, thereby engaging the spring S 1 as shown in Fig.. During the flight phase, an additional small spring S 3 is used to push the foot outside the chain, thereby disengaging the spring S 1. This simple mechanical switch does not require additional control to synchronize the key with the leg state stance or flight which could be difficult to implement, particularly in rough-terrain locomotion where touchdown is hard to predict. The assembled leg is shown in Fig.1; see Table II-B for parameter values. The thigh comprises two lightweight aluminum plates and the shank is formed by a composite material tube to help reduce the weight and the moment of inertia of the leg. Two brushless motors actuate the assembly; one for the knee and one for the hip joint. With the S-PEA design, the knee and hip motors use a 5 : 1 and a 6 : 1 gearbox, respectively. The lower gearbox ratio renders the knee joint more back drivable, and it offers some protection at impacts. To reduce the rotational load on the hip shaft, the knee motor of the S-PEA is placed in proximity to the hip joint, and a cable-pulley system is used to transmit the motion to the knee. TABLE I MECHANICAL PARAMETERS OF THE LEG Parameter Value Units Torso mass (including boom and CPU) (M) 3.55 kg Thigh mass (M 1 ).43 kg Shank mass (M ).73 kg Thigh inertia (including motor) (J 1 ).6 kg m Shank inertia (including motor)(j ). kg m Thigh length (L 1 ).3 m Shank length (L ).37 m Thigh COM to hip distance (L m,1 ).9 m Shank COM to knee distance (L m, ).97 m SPEAR is equipped with proprioceptive sensors providing information on the state of the leg stance or flight and its motion. Two incremental encoders with an accuracy of 14 counts per revolution are used to measure the angular displacements of the motorshafts. Two potentiometers provide absolute measurements of hip and knee joint rotation. The information from the encoders and potentiometers is used to obtain better absolute positions of the joints. Note that since the knee and spring are put in parallel, the deflection of the spring can be easily obtained by measuring the change in joint angle. Finally, a snap-acting switch is located at the foot to detect the state of the leg, stance or flight. C. Stiffness of the Knee Joint Due to the geometry of the kneed leg, the prismatic linear springs S 1 and S effectively correspond to a rotational spring located at the knee joint, see Fig. 3. When the knee rotates an angle θ, thelengthofthespring-cableassembly increases by L = r θ, wherer is the radius of the knee spacer. This change corresponds to the arc length CC shown in Fig. 3. Assuming negligible deformation in the cables, the relation between the rotational spring stiffness and the linear spring stiffness is K Rot = (K Lin L) r = K L Lin r, (1) r where K Lin and K Rot are the stiffnesses of the linear spring and the resulting rotational spring at the joint. A B C C θ Fig. 3. The relation between the linear spring and the corresponding knee rotational spring. The figure depicts the combined effect of S 1 and S. When the mechanical switch engages S 1, the effective rotational stiffness is given by D K Rot = K Lin r = K 1 r, () where r is the radius of the knee spacer. For the chosen K 1 =39N/m and r =1.5in, theequivalentrotational spring stiffness is 56.67Nm/rad. On the other hand,when the key is pushed out of the chain, the springs S 1 and S are connected in series and the effective rotational stiffness is K Rot = K Lin r <K r. (3) For the chosen springs, K =31N/m and r =1.5in, so that the equivalent rotational spring has a stiffness smaller than.3nm/rad,whichissmallenoughtobeneglectedboth in simulations and in experiments. To summarize, due to the switching, the knee joint of the SPEAR has a stiffness of 56.67Nm/rad when the leg is on the ground, acting primarily as an elastic energy storage element during stance. On the other hand, the stiffness of the knee becomes.3nm/rad when the leg is in flight, so that the motors can efficiently prescribe the motion of the leg. D. Adjusting the Stiffness of the Leg The design of SPEAR offers two ways to adjust the stiffness of the leg on line. Thefirstistousethemotor to actively shape the profile of the spring force so that the total stiffness of the joint is determined by the combined D

4 effect of the motor and the passive spring. The second way to tune the knee stiffness is to utilize the geometry of the segmented leg with the S-PEA. In more detail, the linear rotational spring at the knee joint can be viewed as a nonlinear virtual spring applied along the line between the hip and foot; see Fig. 1. Thus, changing the rest angle of the knee spring, changes the stiffness of the virtual spring [16]. Note that the spring is engaged when the foot touches down, hence the touchdown angle determines the rest angle of the knee rotational spring. Since the spring S has a negligible rotational stiffness less than.3nm/rad itis very easy for the knee motor to reset the touchdown angle in flight. This in turn changes the rest angle, and the effective stiffness between the hip and the foot varies accordingly. The virtual spring force - displacement relationship is shown in Fig. 4 for different rest angles of the knee spring. Virtual Spring Force(N) Virtual Spring Deformation(m) Fig. 4. Changing the stiffness of the leg by changing the touchdown angle of knee joint. The effect of the linear rotational spring can be viewed as a virtual nonlinear spring applied between the hip and the toe. Thex-axisis the deformation of the virtual spring, while the y-axis is the forceofthe virtual spring. As the knee becomes more straight (varing from 13 to 1 ), the virtual spring is becoming stiffer. E. Testbed for D Hopping To test the leg in stagittal-plane hopping, a lateral supporting mechanism is designed; see Fig. 5. The test setup has a vertical and a horizontal boom. They allow the leg to move up/down and backward/forward and constrain the lateral movement. Two encoders with 7:1 3D printed gears to amplify their counts are used to measure the rotation of the boom. This information is used to estimate the position of the robot in the D plane for the purposes of control. Note that the horizontal boom adds weight to the torso and does not prevent the robot from falling. III. EXPERIMENTAL RESULTS This section describes experiments that are conducted to verify the performance of the designed S-PEA. The designed controller specifies the torque of the joints during the stance phase and joint position during the flight phase. The results of the experiments show that the parallel spring of the S- PEA reduces both the energy consumed and the peak power required for hopping. Videos of the experiments are also available as part of this paper. Leg Fig. 5. CPU Vertical Boom Horizontal Boom A. Joint Level Control Encoders Batteries The testbed used for D hopping experiments. The two actuators of the leg have current control ability. Using a digital-to-analog converter, the reference current is sent to the motor servo controller and followed by the built-in current loop (khz). The current of the motor is measured by the motor servo and sent back to the CPU. Using the measured current, the torque of the joint is estimated and used hereafter to estimate the mechanical power of the motor. With the ability to switch off the spring at the knee, the joint position during flight is controlled using the a Linear Quadratic Regulator (LQR). Figure 6 shows the step response of the knee joint and the current for the case where the energy storing spring S 1 is not engaged; i.e., the leg is in flight. Note that if the spring S 1 were not switched off, the knee motor would have to generate 8Nm (corresponding to 7A) for the commanded.5rad rotation. Knee Angle(rad) Knee Current(Amp) Fig. 6. : Position control experiment of the knee joint. The red solid line is a simulation result, which matches the experiment. : The reference current (dotted line) and the measured current for the position control. B. Hopping in Place 1) Hopping Controller: One complete hopping motion of the monopod is composed of a flight phase and a stance phase. The leg enters the stance phase when the foot touches down with the ground. This event is captured by the switch installed at the foot. The leg lifts off to enter its flight phase when the ground reaction force becomes zero and the acceleration of the toe is directed upwards. With the knee and hip joints controlled, the liftoff event can be specified so that it occurs when the knee reaches a pre-specified angle

5 which is taken equal to the touchdown angle. This way the energy stored in the spring S 1 is returned to the system. The designed controller has different objectives during the stance and flight phases. During stance, the torques of the hip and knee joints are controlled with the purpose of (i) injecting energy to the system, and (ii) preventing slipping. During flight on the other hand, the angular positions of the hip and knee joints are controlled to stabilize the system using a modified version of Raibert s velocity controller [3]. In more detail, to sustain continuous hopping, the knee motor compensates during the stance phase for the energy lost due to impact and friction as follows. In the first half of the stance phase, the motor further compresses the spring S 1 injecting energy as needed, while in the second half, the motor assists with spring recoil preparing the system for takeoff. This action is captured by commanding the following torque to the knee actuator { τ τ knee [k +1]= knee α 1 (y y[k]), if t t TD < Tst α 1 (y y[k]) τknee, if t t TD Tst (4) where τknee is a constant corresponding to the nominal knee torque for a periodic hopping gait with a hip apex height y, y[k] is the apex height at the k-th step, t TD is the touchdown instant, and T st is the total duration of the stance phase. Note that (4) ensures that the knee actuator only does positive work during stance. The hip actuator applies a small torque τ Hip = τ Hip, (5) which is kept constant throughout the stance phase with the purpose of reducing the chance of slipping. During flight, a modified version of Raibert s velocity controller [3] is used to adjust the hip joint angle keeping the knee angle constant. In more detail, the knee joint is commanded to a constant, i.e., θ Knee =Θ Knee,whilethehip angle which determines the touchdown angle γ in Fig. 1 isadjustedaccordingtotheprescription θ Hip = θ Hip α ẋ cm, (6) where α is a constant gain, θhip is the nominal value of the hip angle and ẋ cm is the measured horizontal velocity of the leg s center of mass at flight phase. In implementing this controller, the angle of rotation of the vertical boom of Fig. 5 is used to estimate the average horizontal velocity by dividing it with the time duration of the step. Note that as was mentioned in Section II-D, the touchdown angle of the knee determines the stiffness of the leg during the subsequent stance phase and has a great influence both on the stability and energy efficiency of hopping. We do not make use of this capability here; however, controllers that take advantage of variable stiffness are the subject of ongoing work. ) Experimental Results: The experimental results of stable hopping are shown in Fig. 7. The hop is initialized at t = s,byfirstbendingitskneetostoreenergyinthe spring S 1,andthenpushingagainstthegroundwhentheleg is at the bottom of its stance to cause liftoff. After a few seconds, the leg is stabilized to a periodic hopping motion. Vertical Position(m) Fig. 7. Vertical displacement of the hip for the hopping in place experiment. Figure 8 depicts the evolution of some variables of interest during one stride of the hopping motion realized by the control procedure described above. As Fig. 8 shows, the knee spring attains its maximum deformation of.8rad at the middle of the stance phase, storing about 18J energy. Fig. 8(c) shows the current of the knee actuator, which during the stance phase is kept constant and equal to 5.5A approximately corresponding to a knee torque of about 5.7Nm albeitswitchingsignaccordingto(4).notethatthe knee actuator only injects about 4.6J of mechanical energy during the first half of the stance phase indicating that part of the gravitational potential energy and kinetic energy is recovered through the spring S 1. Hip Angle(rad) Knee Current(Amp) (c) Knee Angle(rad) Knee Power (Watt) Fig. 8. Experimental results of hopping in place. The red dotted line is the reference signal. The vertical lines stands for the liftoff event. Hip angle. Knee angle. (c) The current of the knee actuator. (d) The power of knee motor (blue line) and the spring (red line) at one stride. Figure 8(d) shows the power of the spring and of the knee actuator for reasons of comparison. It can be seen that the power of the knee motor reaches its peak of 8W at the beginning of the stance phase when the motor injects energy. Note also that during stance the knee motor only does positive work, which is a result of the controller design (4). During the same phase, the power associated with the knee spring S 1 reaches a peak of W during compression and 4W during decompression, much larger than the peak power of the knee actuator. In fact, the power required by the knee motor is kept small throughout the stance phase, (d)

6 owing to the energy recovery offered by the spring. To characterize the mechanical energy storage efficiency, we adopt the metric defined in [17]; i.e., T η := 1 max(p motor, )dt T max(p, (7) joint, )dt where T is the duration of the stride, P motor is the total power of the knee and hip motors, and P joint is the mechanical power of the joints. The coefficient η effectively measures how much of the positive mechanical energy used in one hopping stride can be provided passively. For the designed leg, η =.64, indicatingthat64% of the positive mechanical energy at one stride is generated by the spring. C. Forward Hopping Forward hopping is realized by a slight modification of (6), which now becomes θ Hip = θ Hip α 3 (ẋ cm ẋ cm ), (8) where ẋ cm is the desired horizontal velocity of the hip during flight phase. Experimental results for forward hopping are given in Fig. 9. In this experiment, the robot s forward speed was.14m/s approximately, with a stride duration equal to.58s.similarlytothehopping-in-placeexperiments of Section III-B., the knee spring S 1 recycles part of the mechanical energy during the stance phase, keeping the power requirements from the knee motor small. This can be seen in Fig. 9(d), which is similar to what was observed in the hopping-in-place experiments. Compared with hopping in place, forward running results in larger deformations of the knee spring and higher amplitude of the vertical oscillation. Horizontal Position(m) Knee Angle(rad) (c) Vertical Position(m) Knee Power (Watt) Fig. 9. Experimental results of a forward hopping gait. The horizontal displacement of the hip. The vertical displacement of the hip.(c) Knee angle; the red dotted line is the reference position. (d) The power of knee motor (blue line) and the spring (red line) at one stride. The vertical lines in (c) and (d) represents the liftoff event. IV. CONCLUSION This paper introduced SPEAR, a two-dof leg designed with a Switchable Parallel Elastic Actuator (S-PEA) at its (d) knee joint. At the stance phase, the spring in the knee works in parallel with the actuator to recover energy, reducing the peak torque and power requirements of the actuator. At the flight phase, the spring is switched off from the system to allow better motion control of the joint. The proposed design is compact and reliable. By placing the switch on the foot, the spring is synchronized naturally with the hopping motion without the need of an additional actuator. Experimental results demonstrate that the S-PEA driving the knee joint recycles part of the energy during hopping and helps reducing the peak torque and power requirements of the motor. REFERENCES [1] R. v. Ham, T. G. Sugar, B. Vanderborght, K. W. Hollander, and D. Lefeber, Compliant actuator designs, Robotics & Automation Magazine, vol.16,no.3,pp.81 94,9. [] G. Pratt and M. 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